Answer:
720 degrees.
Step-by-step explanation:
The sum of the interior angles of a convex polygon with n sides is
180(n - 2) degrees.
In this case, n = 6 sides, so the angle sum is
180(6 - 2) = 180(4) = 720 degrees.
The reason this works is that if you draw a diagonal from one vertex to the others (see attached image), you get 2 fewer triangles than the number of sides. Each triangle contains a total of 180 degrees, so the total of all the interior angles is 180(n - 2).
Answer:
x = 34 degrees
Step-by-step explanation:
Each solid line and triangle add up to 180, so start from the left and slowly do your math.
180 - 112 = 68
180 - 68 - 43 = 69
180 - 69 = 111
180 - 111 - 35 = 34
x and the last angle are the same.
For this, we use simultaneous equations. Let George's page be g, Charlie's be c and Bill's page be b.
First, <span>George's page contains twice as many type words as Bill's.
Thus, g = 2b.
</span><span>Second, Bill's page contains 50 fewer words than Charlie's page.
Thus, b = c - 50.
</span>If each person can type 60 words per minute, after one minute (i.e. when 60 more words have been typed) <span>the difference between twice the number of words on bills page and the number of words on Charlie's page is 210.
We can express that as 2b - c = 210.
Now we need to find b, since it represents Bill's page.
We can substitute b for (c - 50) since b = c - 50, into the equation 2b - c = 210. This makes it 2(c - 50) - c = 210.
We can expand this to 2c - 100 - c = 210.
We can simplify this to c - 100 = 210.
Add 100 to both sides.
c - 100 + 100 = 210 + 100
Then simplify: c = 210 + 100 = 310.
Now that we know c, we can use the first equation to find b.
b = c - 50 = 310 - 50 = 260.
260 is your answer. I don't know where George comes into it. Maybe it's a red herring!</span>
Answer:
37.20 %
Step-by-step explanation:
Circumference = 2 × pi × r
30 = 2 × 3.14 × r
r = 4.7770700637
Area of her face = pi × r²
3.14 × 4.7770700637²
= 71.6560509556 in²
Area of the mask = 9 × 5 = 45 in²
Uncovered area
= 71.6560509556 - 45
= 26.6560509556 units²
% of uncovered area:
26.6560509556/71.6560509556 × 100
37.2%
